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We study Virasoro minimal-model 4-point conformal blocks on the sphere and0-point conformal blocks on the torus (the Virasoro characters), as solutionsof Zamolodchikov-type recursion relations. In particular, we study thesingularities due to resonances of the dimensions of conformal fields inminimal-model representations, that appear in the intermediate steps of solvingthe recursion relations, but cancel in the final results.

Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models